Linear preservers for matrix inequalities and partial orderings

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Abstract

We characterize the linear preservers of minus partial order on matrix algebras. The developed approach allows us to classify linear transformations that live fixed several matrix relations arising as extremal cases in some classical matrix inequalities, including rank-additivity relation and related properties. Applications to the determinant preservers are considered.

Original languageEnglish
Pages (from-to)75-87
Number of pages13
JournalLinear Algebra and Its Applications
Volume331
Issue number1-3
DOIs
StatePublished - 1 Jul 2001
Externally publishedYes

Bibliographical note

Funding Information:
This work is partially supported by RFBR Grants NN. 00-15-96128 and 99-01-00382. E-mail address: [email protected] (A. Guterman).

Funding

This work is partially supported by RFBR Grants NN. 00-15-96128 and 99-01-00382. E-mail address: [email protected] (A. Guterman).

FundersFunder number
Russian Foundation for Basic Research

    Keywords

    • Linear preservers
    • Minus-order
    • Rank additivity

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